Some q‐rung orthopair uncertain linguistic aggregation operators and their application to multiple attribute group decision making

q‐Rung orthopair fuzzy sets (q‐ROFSs), originally presented by Yager, are a powerful fuzzy information representation model, which generalize the classical intuitionistic fuzzy sets and Pythagorean fuzzy sets and provide more freedom and choice for decision makers (DMs) by allowing the sum of the qth power of the membership and the qth power of the nonmembership to be less than or equal to 1. In this paper, a new class of fuzzy sets called q‐rung orthopair uncertain linguistic sets (q‐ROULSs) based on the q‐ROFSs and uncertain linguistic variables (ULVs) is proposed, and this can describe the qualitative assessment of DMs and provide them more freedom in reflecting their belief about allowable membership grades. On the basis of the proposed operational rules and comparison method of q‐ROULSs, several q‐rung orthopair uncertain linguistic aggregation operators are developed, including the q‐rung orthopair uncertain linguistic weighted arithmetic average operator, the q‐rung orthopair uncertain linguistic ordered weighted average operator, the q‐rung orthopair uncertain linguistic hybrid weighted average operator, the q‐rung orthopair uncertain linguistic weighted geometric average operator, the q‐rung orthopair uncertain linguistic ordered weighted geometric operator, and the q‐rung orthopair uncertain linguistic hybrid weighted geometric operator. Then, some desirable properties and special cases of these new operators are also investigated and studied, in particular, some existing intuitionistic fuzzy aggregation operators and Pythagorean fuzzy aggregation operators are proved to be special cases of these new operators. Furthermore, based on these proposed operators, we develop an approach to solve the multiple attribute group decision making problems, in which the evaluation information is expressed as q‐rung orthopair ULVs. Finally, we provide several examples to illustrate the specific decision‐making steps and explain the validity and feasibility of two methods by comparing with other methods.